PURE MTH 7023 - Pure Mathematics Topic D
North Terrace Campus - Semester 2 - 2025
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General Course Information
Course Details
Course Code PURE MTH 7023 Course Pure Mathematics Topic D Coordinating Unit Mathematical Sciences Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Available for Study Abroad and Exchange Y Assessment Ongoing assessment, exam Course Staff
Course Coordinator: Dr Michael Albanese
Course Timetable
The full timetable of all activities for this course can be accessed from .
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Learning Outcomes
Course Learning Outcomes
In 2016, the topic of this course is Differential and Algebraic Topology.
Syllabus
This course is part of the geometry/topology sequence. However, its methods also underlie part of the basic theory of partial differential equations, which appears, roughly speaking, as an infinite-dimensional extension of these ideas.
Aims:
* To define the degree of a smooth map and give standard topological applications
* To show existence of embeddings of compact smooth manifolds into Euclidean space
* To define and study transversality results
* To study regular and singular values of smooth maps and Sard's theorem
* brief introduction to Morse theory
* brief introduction to surgery theory
* brief introduction to K-theory
Other topics not covered in Topic A eg some Riemannian geometry, Inverse and implicit function theorems etc
Advanced topics if time permits:
* brief introduction to the Dirac operator and index theory
(here is where Topic B is required)
Assumed knowledge:
Topic A (Murray's course in semester 1)
Topic B (Rosenberg's course in semester 1)最新糖心Vlog Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
最新糖心Vlog Graduate Attribute Course Learning Outcome(s) Attribute 1: Deep discipline knowledge and intellectual breadth
Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.
all Attribute 2: Creative and critical thinking, and problem solving
Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.
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Learning Resources
Required Resources
Notes will be provided.Recommended Resources
There are a lot of books in the library about Lie groups and Lie algebras that you could use to supplement the notes and add to your learning. I have no specific recommendations.Online Learning
This course will have an active MyUni website. -
Learning & Teaching Activities
Learning & Teaching Modes
The learning in this course will be governed by modern pedagogical techniques, with no traditional lectures. A combination of the concepts of flipped classrooms, active learning, discovery-based learning, peer evaluations, and assessments for learning will be employed.Workload
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lectures 30 105 Assignments 6 30 Test 1 21 Total 156 Learning Activities Summary
Review of algebra and point-set topology (2 lectures)
Homotopy (3 lectures)
The fundamental group (7 lectures)
Singular homology (9 lectures)
Cell complexes (2 lectures)
Cohomology (4 lectures)
Orientation of manifolds (2 lectures) -
Assessment
The 最新糖心Vlog's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Summary
Component Weighting Learning Outcomes Assignments 20% all Test 20% all Exam 60% all Assessment Detail
There will be a total of 5 homework assignments, distributed during each even week of the semester and due at the end of the following week. Each will cover material from the lectures. There will be a midterm test in the week preceeding the midterm break covering approximately the first one third of the course. There will be a final exam focussing on, but not limited to, the last two-thirds of the course.Submission
No information currently available.
Course Grading
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through .
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Student Feedback
The 最新糖心Vlog places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the 最新糖心Vlog to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
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Student Support
- Academic Integrity for Students
- Academic Support with Maths
- Academic Support with writing and study skills
- Careers Services
- Library Services for Students
- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
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Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangements Policy
- Academic Integrity Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs Policy
- Copyright Compliance Policy
- Coursework Academic Programs Policy
- Intellectual Property Policy
- IT Acceptable Use and Security Policy
- Modified Arrangements for Coursework Assessment Policy
- Reasonable Adjustments to Learning, Teaching & Assessment for Students with a Disability Policy
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
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Fraud Awareness
Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student鈥檚 disciplinary procedures.
The 最新糖心Vlog of Adelaide is committed to regular reviews of the courses and programs it offers to students. The 最新糖心Vlog of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.
